Abstract

In this paper different topologies of populations of FitzHugh–Nagumo neurons have been introduced in order to investigate the role played by the noise in the network. Each neuron is subjected to an independent source of noise. In these conditions the behavior of the population depends on the connection among the elements. By analyzing several kinds of topology (ranging from regular to random) different behaviors have been observed. Several topologies behave in an optimal way with respect to the range of noise level leading to an improvement in the stimulus response coherence, while others with respect to the maximum values of the performance index. However, the best results in terms of both the suitable noise level and high stimulus response coherence have been obtained when a diversity in neuron characteristic parameters has been introduced and the neurons have been connected in a small-world topology.

Received 11 December 2004Accepted 13 January 2005Published online 21 March 2005

Lead Paragraph: The dynamics of neurons is often modeled by using differential equation models. Networks of many neurons can be studied by connecting many of these models and studying the global behavior of the system. The importance of these studies is related to a deep understanding of the neural mechanisms underlying neural systems. This paper focuses on several topological structures of networks of these models and studies how they behave when noise is present. Usually (i.e. in linear systems), the presence of noise has negative effects on the behavior of the system. In nonlinear systems (as neuron models are), noise may play a constructive role. In this paper we show how the configuration that most benefits from the introduction of noise is that obtained connecting nonidentical neurons in a structure which has both regular local connections and long-range random connections.

Acknowledgments:

This work was partially supported by the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca” (MIUR) under Firb Project No. RBNE01CW3M.